Thrust Layout Optimization for Masonry Structures

Form-resistant structures are efficient structural systems that can contribute to addressing the adverse climate impacts of the construction industry by reducing material usage. Also, the availability of improved assessment and strengthening methods for masonry form-resistant structures can extend the life of many ageing buildings and other structures, ensuring these are not needlessly replaced at great cost to the planet.

Building on an observation by Hooke, Heyman’s ‘safe theorem’ has been widely used to assess the safety of form-resistant structures. However, Heyman used a funicular thrust line to represent equilibrium, which has been found to be problematic in some cases. Seeking to improve upon the funicular thrust line, the notion of a ‘thrust layout’ is presented here. This can accurately represent the state of equilibrium while also enabling visualization of the flow of forces within a form-resistant structure. This is achieved by explicit consideration of block stereotomy and more realistic treatment of tensile forces.

A new automated analysis procedure, termed thrust layout optimization (TLO), is presented to allow identification of thrust layouts in masonry gravity structures comprising general arrangements of masonry blocks. The procedure employs a modified truss layout optimization with transmissible loads formulation and allows explicit consideration of sliding failures. A range of examples that demonstrate the efficacy of the TLO procedure are presented; these show that thrust line bifurcations can be automatically identified in problems involving openings, and that there is no need to estimate the ‘ineffective area’ in buttress wall problems, both issues encountered when using the traditional thrust line analysis method.

The TLO procedure is then extended to determine the optimal placement of auxiliary strengthening measures. While current practice is to use engineering intuition to determine the placement of strengthening measures, TLO provides a more robust physics-based approach, with clear visualization of force flows in strengthened structures.